This invention relates to analogue-to-digital converters, and especially to sigma-delta analogue-to-digital converters.
Sigma-delta analogue-to-digital converters include quantising means for producing a digital output, oversampled relative to the signal bandwidth, and a feedback path for feeding a signal derived from the digital output to be combined in analogue form with the analogue input for input to filter means, the output of the filter means being applied to the quantising means. This permits improved signal-to-noise ratio to be achieved from coarse quantisation by shaping the quantisation noise spectrum to suppress it within a desired bandwidth.
The extent to which the quantising noise is shaped in the signal passband depends upon the order of the loop filter within the sigma-delta analogue-to-digital converter, the depth of the null in the quantising noise increasing as the order of the loop filter increases. Thus, referring to FIG. 1, a third order bandpass sigma-delta analogue-to-digital converter is theoretically possible. An analogue input 1 is combined at summing node 2 with an analogue version, due to digital-to-analogue converter 3, of the digital output 5, which is fed back along a negative feedback path 6, to produce a difference signal in the form of a current which flows in the first stage 7 of the filter means. Each stage 7, 8, 9 the filter means consists of a resonant circuit (inductor and capacitor in parallel) connected to a series resistor. The resulting voltage appears at the input of voltage-to-current converter buffer amplifier 10 producing a current at its output which flows in the second stage 8 of the filter, likewise producing a voltage input to a voltage-to-current converter buffer amplifier 11. Similarly, an output current flows in the third stage 9 of the filter means which causes a voltage to be applied to the voltage-to-current converter buffer amplifier 12, the output current of which develops across a resistor (not shown) a voltage at the input of quantising means 13.
The voltage across the third stage 9 of the filter means in response to an input analogue current depends upon the voltage across the second stage 8 of the filter means which in turn depends upon the voltage across the first stage 7. The response of each stage can perhaps best be understood by considering the effect of a pulse input current at summing node 2, imagining the forward path to be broken just before quantising means 13.
Referring to FIG. 2, the output voltage of the first filter stage 7 in response to a pulse input at the analogue input 1 can be considered to be formed of two parts, namely, 7a, a pulse voltage due to the resistor and a voltage 7b, which rises over the width of the pulse and then continues sinusoidally with approximately constant amplitude (actually slowly exponentially decaying).
The resulting voltage across the second stage of the filter means can be considered as being made up of four components 8a-8d. The voltage pulse 7a causes a voltage pulse 8a across the resistor and a rising and thereafter sinusoidal response 8b across the resonant circuit (like voltage 7b for the first stage). The voltage 7b causes a similar voltage 8c across the resistor, but a sinusoidal voltage across the resonant circuit which has a linearly increasing amplitude 8d.
The resulting voltage across the third stage 9 of the filter can be considered as formed of the components 9a-9f. The pulse voltage 8a causes a similar pulse voltage 9a across the resistor and a rising and thereafter sinusoidal voltage 9b (like 7b) across the resonant circuit. The voltages 8b, 8c are of the same form, and their combined effect is to produce a similar voltage 9c across the resistor, and a sinusoidal voltage having linearly increasing amplitude 9d (like 8d) across the resonant circuit. The voltage 8d produces a similar voltage 9e across the resistor and a sinusoid 9f having an amplitude increasing according to a square law across the resonant circuit.
The response of the filter means to a step input hence consists of six components (or eight if 8a, b are considered separately). However, there are four components only when voltages of similar form are considered as one component, namely, a first order response 9b, 9c consisting of a rising portion followed by sinusoidal portion of approximately constant amplitude, a second order response 9d, 9e consisting of a rising portion of shallower slope and sinusoidal portion of linearly increasing amplitude, a third order response 9f consisting of a rising portion of shallower slope and a sinusoidal portion, the amplitude of which increases according to a square law, and a zeroth order response formed by the pulse response 9a.
To obtain a desired response of the filter means of FIG. 1, the values of the resistors, relative values of the inductor and capacitor of each resonant circuit (the product of the values must be such as to produce the desired resonant frequency), and the amplifications of the buffer amplifiers must be selected accordingly. It is in fact very difficult to make such a converter work except over restricted ranges of operation. The Applicants themselves encountered these difficulties in attempting to design a second order bandpass sigma-delta analogue-to-digital converter (FIG. 4 of EP-A-O 399 738).
In one proposal concerning a second order bandpass sigma-delta converter (Electronics Letters, vol. 26, no. 20, 27 September 1990, pages 1652-3, H.-J. Dressler "Interpolative Bandpass A/D Conversion--Experimental Results"), these difficulties have been to some extent alleviated. The filter means of the sigma-delta converter comprises two stages, and the filtered signal which is fed to the quantising means of the analogue-to-digital converter, is derived using the output of the second stage which is representative only of the response of the second filter order and not of other filter orders. This output is combined with the output of the first stage of the filter (which is fed along a separate signal path) to produce the said filtered signal.
Whilst this concept in theory may be extended to three filter stages, so that the output of the third stage is representative only of the third order response, or more than three filter stages, and whilst a larger number of filter stages is desirable in any case from the point of view of suppressing quantising noise in the passband of the analogue-to-digital converter, a problem arises. This is that phase shifts across each stage combine so that negative feedback via the feedback loop can become positive feedback. Then, in the event of overload, the analogue-to-digital converter could fail to recover.